You do not need a carnet to get to Kaz. No one will ask you for one.
A "real" green card insurance will take as far as the Ukraine. After that you buy it at the borders. The bit of paper the UK insurers give you, counts for nothing outside of the EU.
If you buy the bike new in the UK, buy it for export and save the 17.5%VAT as your destination is a non-EU country. If its like other EU states, you can use it in the UK for a fixed period of time before you leave. If its not gone by that date, you will have to stump up the tax.
If you buy second-hand from a dealer, there is also a VAT saving but you may have to try and get that back after the bike has gone. Which you will have to prove.
I seem to remember big bikes are expensive in Almaty... you may pay a lot of import tax
John